While the term filter may be broadly used to describe any of a class of components or systems that separate and attenuate the passage of certain portions of an input to the filter, the present invention is primarily concerned with filters used in electronic systems to produce a predetermined frequency-amplitude output and a desired phase relationship for that output. Analogous concepts may also be used to configure filters in the electro-magnetic spectrum, including light waves, provided that the appropriate component choices are made. Soon after the development of practical electronic circuits, it became obvious that means to filter a signal in order to enhance some frequencies and suppress others would be desirable. Classical filtering techniques led to the development of the theory of tuning circuits in the late 19th century and the resonance circuits developed during that time played a significant role in the development of the radio and the telephone. As electronic systems became more sophisticated, filter designs improved beyond their simple forms to include more complex circuits incorporating resistors, inductors and capacitors (RLC) components. While circuits incorporating such components approached new levels of sophistication, they were still passive in that the component characteristics were unalterable by electronic control. One important characteristic of such passive filters was that they could be described by a mathematical expression of their frequency behavior consisting of linear, lumped parameter equations. Further development of filter design for electronic circuits included the addition of active components such as amplifiers which allowed the elimination of inductors, thereby substantially reducing the weight and size of many of the filters. Such active-RC filters became widely used in a variety of advanced electronic systems including many in current use.
Statistical filtering theory has been developed to improve signal detection of complex electro-magnetic signals. Previous work in filter theory assumed that a signal of interest could be separated from an undesired signal based on the desired signal's frequency, since the frequencies composing the desired signal were substantially different from those of the unwanted signal. However, such approaches proved inadequate when the frequency content of both signals overlapped or when statistical information concerning the signals was unavailable. While some solutions to this problem were adequately addressed by an assumption of stationary statistics of the signal being detected, it was not until the development of the Kalman time domain, steady state filter theory was developed, that an adequate solution was available for such statistically based filtering of information signals.
Meanwhile, the rapid development of digital computers led to the development of digital filtering theories that could operate on digital signals. Naturally, a large part of the early work in digital filters focused on building good approximations of existing analog filters. Soon, however, it became evident that the development of efficient algorithms for calculating the discrete Fourier transform would allow the development of many previously unavailable filter capabilities.
An important application for filters in modern electronic systems is the filtering of signals in such a way that the output spectrum amplitude-frequency content may be chosen by the designer and a phase shift relationship across the frequency spectrum may also be specified. The mathematical expression of such a digital filter is similar to the passive analog component filter type linear, lumped parameter equations. While such filters have provided sophistication and capabilities beyond those which were achievable with the passive element and active element types previously available, they have nonetheless tracked improvements in digital components and digital computers and often merely represent a digital implementation of the previous theories. Because of the speed limitations of multipliers used in active digital or analog filter systems, a current problem in filter design involves the development of efficient methods for designing filters that may be fabricated with a minimum number of multipliers or with multipliers of unity coefficient. These approaches have included methods to reduce the magnitude of the multiplication load demanded of the filtering elements and the inclusion of finite impulse response elements in order to build filters that have a multiplierless implementation. While such approaches have been suggested, they have either been limited by their ability to perform demanding filtering functions or, in the alternative, have required the use of multiplier filter elements which, while not of high multiplication factors, nonetheless require the inclusion of numerous non-unity multiplier elements.
While the above developments have improved the ability of designers to configure filter systems with improved amplitude-phase performance, the mathematical expressions for such filters are still linear, lumped parameter forms that limit the capabilities of such filters. There remains, therefore, a continuing need for filters that employ only delay elements and addition or subtraction elements and which may be simply and easily designed and implemented while retaining high performance in the filtering process.